Binary Operation Boolean Logic
Transcript of Binary Operation Boolean Logic
Lecture 5Binary Operation
Boolean Logic
Lecturer: Sumaira Hussain
S.M.I university
Binary Operations
• Addition• Subtraction • Multiplication• Division
Addition
Subtraction
Multiplication
Division
Boolean Logic OperationsLet x, y, z be Boolean variables. Boolean variables can only have binary values i.e., theycan have values which are either 0 or 1.
For example, if we represent the state of a light switch with a Boolean variable x, we will assign a value of 0 to x when the switch is OFF, and 1 when it is ONA few other names for the states of these Boolean variables
0 1Off OnLow HighFalse True
Boolean Logic
• AND• OR• NOT
We define the following logic operations or functions among the Boolean variables
Name Example SymbolicallyNOT y = NOT(x) x´AND z = x AND y x · yOR z = x OR y x + y
Truth Table
A truth table defines the output of a logic function for all possible inputs.
Number of rows in a truth table?2nn = number of input variables
NOT Operation
Truth Table for the NOT OperationX y = x´0 11 0
AND Operation
Truth Table for the AND OperationX y z = x · y0 0 00 1 01 0 01 1 1
OR OperationTruth Table for the OR Operation
x y z = x + y0 0 00 1 11 0 11 1 1
Examples
z = (x + y)´
x y x + y z = (x + y)´0 0 0 10 1 1 01 0 1 01 1 1 0
Examples
z = y · (x + y)
x y x + y z = y · (x+ y)0 0 0 00 1 1 11 0 1 01 1 1 1